Definition:Linear Continuum
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Definition
A totally ordered set $\struct {S, \preceq}$ is a linear continuum if and only if:
- $(1): \quad \struct {S, \preceq}$ is densely ordered
- $(2): \quad \struct {S, \preceq}$ is Dedekind complete
Sources
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers